1. ## Distance help

Can someone help explain how to do this problem?

Pizza Delivery Problem
: Ida Livermore starts off on her route. She records her truck's speed, v(t), in mi/hr, at various times, t, in seconds, since she started.

v(t)=5t^(½)

Approximately how far did Ida's truck travel from t=1 to t=9?

2. What do you know about these three guys?

s(t) - Position
v(t) - Velocity
a(t) - Acceleration

????

That is their usual names, anyway.

Derivative move down the list. Antiderivative move up. Which do you need.

3. Originally Posted by TKHunny
What do you know about these three guys?

s(t) - Position
v(t) - Velocity
a(t) - Acceleration

????

That is their usual names, anyway.

Derivative move down the list. Antiderivative move up. Which do you need.
Well, I know that you need find the derivative, but I don't understand how to get the answer of 127 feet. (I looked up the answer in the back of my book.)

**When I did the problem, I got 86.2 for my derivative.

4. Originally Posted by Cursed
Well, I know that you need find the derivative, but I don't understand how to get the answer of 127 feet. (I looked up the answer in the back of my book.)

**When I did the problem, I got 86.2 for my derivative.
I don't understand why find the derivative.
It should be integration.

V(t) is in mi/hr, while t is in seconds. And the book answer is in feet.
The units don't tally.

Convert mi/hr into ft/sec.
(1mi/1hr)(5280ft/1mi)(1hr/3600sec) = (5280)/(3600) = 1.4667 ft/sec

So the
V(t) in mph = 5*t^(1/2)
should be
V(t) in ft/sec = (5*1.4667)t^(1/2)

S = (5*1.4667)INT.(1-->9)[t^(1/2)]dt
S = (7.333)(2/3)[t^(3/2)]|(1-->9)
S = (4.888)[9^(3/2) -1^(3/2)]
S = (4.888)[27 -1]
S = 127.088
or
S = 127 ft.